Propositional Logic and Operators

Example: Consider the following implication:

If it is raining, then the ground is wet.

Symbolically, let $p = \;($"$\text{it is raining}$"$)$ and $q = \;($"$\text{the ground is wet}$"$)$. Then, the implication is written as $p \to q$.

The converse ($q \to p$) of this statement is:

If the ground is wet, then it is raining.

The converse is not always true. The ground could be wet for other reasons (e.g., someone watered the lawn).

On the next slide, we bring the corresponding examples for the inverse and contrapositive statements.